Large-scale tight-binding simulations of quantum transport in ballistic graphene

Abstract

Graphene has proven to host outstanding mesoscopic effects involving massless Dirac quasiparticles travelling ballistically resulting in the current flow exhibiting light-like behaviour. A new branch of 2D electronics inspired by the standard principles of optics is rapidly evolving, calling for a deeper understanding of transport in large-scale devices at a quantum level. Here we perform large-scale quantum transport calculations based on a tight-binding model of graphene and the non-equilibrium Green's function method and include the effects of p-n junctions of different shape, magnetic field, and absorptive regions acting as drains for current. We stress the importance of choosing absorbing boundary conditions in the calculations to correctly capture how current flows in the limit of infinite devices. As a specific application we present a fully quantum-mechanical framework for the '2D Dirac fermion microscope' recently proposed by Bøggild et al (2017 Nat. Commun. 8 10.1038), tackling several key electron-optical effects therein predicted via semiclassical trajectory simulations, such as electron beam collimation, deflection and scattering off Veselago dots. Our results confirm that a semiclassical approach to a large extend is sufficient to capture the main transport features in the mesoscopic limit and the optical regime, but also that a richer electron-optical landscape is to be expected when coherence or other purely quantum effects are accounted for in the simulations.

Multi-scale approach to first-principles electron transport beyond 100 nm

“…sisl is a Python package used to create and/or manipulate DFT and TB models for arbitrary geometries, with any number of orbitals and any periodicity. [56] The device Green's function in TBtrans is generally implemented as:…”

Electrostatic superlattices on scaled graphene lattices

“…The method can be immediately applied to take into account, for example, complex local gating or multi-probe transport, in order to make further analysis for transport experiments or even reliable predictions. We note some recent studies working on developing numerical techniques that allow large-scale efficient transport simulations [47][48][49], but scaling the graphene lattices with an appropriately chosen scaling factor depending on the superlattice periodicity seems to be of least technical complexity and is readily applicable to anyone who is familiar with quantum transport using, for example, real-space Green's function method [32] or the popular open-source python package KWANT [50].…”

Chebyshev polynomial method to Landauer–Büttiker formula of quantum transport in nanostructures

“…(17)]; Second, inclusion of them into the conductor's Green's function as Eq. (16). The numerical treatments of these steps by direct matrix calculations have been very mature and well-known 4,13 .…”

“…Afterwards, they are inserted into Eqs. (16), (20) and finally (19) for the evaluation of the transmission. In this process, the most time-consuming step will be the calculation of lead self energies, and the matrix inversion (which does not preserve the sparseness of the matrix) in Eq.…”

“…In this process, the most time-consuming step will be the calculation of lead self energies, and the matrix inversion (which does not preserve the sparseness of the matrix) in Eq. (16). For a two-terminal device simulation where the conductor lattice can be well divided into layers of sites (layers should be defined in such a way that hoppings only exist between nearest layers), the simulation can be decomposed into a layer-to-layer recursive method, which is based on the Dyson equation for Green's functions 13,47 .…”